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Zhang et al. J. Mater. Inf. 2026, 6, 11 Page 13 of 17

To further quantify the relative importance of these descriptors, SHAP analysis was applied to trained
regression models for each oxide family, as shown in Figure 7C. For RE TaO , dominant predictive features
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include RE–O E , bond-length disorder (D ), and E form - consistent with the physical picture of
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configurational complexity and bond robustness as key regulators of performance. In RE Zr O , the most
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influential features shift slightly to Zr–O E , Bader charge disorder, and V 0, emphasizing the role of atomic
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packing and local charge environment. Taken together, both correlation-based and model-based analyses
converge on three dominant descriptors: E , D and Bader charge heterogeneity (D ), as the primary
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determinants of K and κ across the RE series. These interpretable, physically grounded parameters
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elucidate the mechanisms of phonon scattering, lattice stiffening and crack resistance. Moreover, they serve
as a robust foundation for data-driven materials design. Importantly, these insights explain why RE TaO 7
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oxides, despite exhibiting intrinsically lower thermal conductivity, maintain moderate toughness. The
reinforcement of RE–O bonds and local disorder-induced energy dissipation mechanisms helps compensate
for structural complexity. In contrast, RE Zr O oxides achieve a superior balance of high fracture resistance
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and moderate κ , attributable to their chemically ordered and structurally accommodating lattice framework.
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CONCLUSIONS
In this work, a comprehensive data-driven framework was employed to investigate the thermomechanical
performance of RE TaO and RE Zr O oxides, aiming to guide the rational design of advanced TBC
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materials. First-principles calculations and model-based analyses were used to evaluate their structural
stability, thermal conductivity, and intrinsic K across the RE series. The results reveal that RE TaO exhibits
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consistently lower κ than RE Zr O , primarily due to its lower crystallographic symmetry, heavier atomic
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constituents, and higher degree of structural disorder. In contrast, RE Zr O displays slightly higher intrinsic
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K , which is attributed to its ordered vacancy sublattice and more symmetric bonding environment.
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However, this theoretical trend differs from experimental observations, where RE TaO ceramics often
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demonstrate comparable or higher K , likely due to extrinsic microstructural effects such as porosity,
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residual stress, and grain boundary interactions, which are not captured in idealized simulations. To uncover
the underlying structure–property relationships, both Pearson correlation and SHAP analyses were
conducted, highlighting E , charge disorder and bond-length heterogeneity as the most influential
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descriptors governing κ and K . These insights not only reconcile theoretical predictions with experimental
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data but also provide a predictive framework for identifying and optimizing RE oxide compositions with
balanced mechanical integrity and thermal insulation performance for high-temperature applications.
DECLARATIONS
Acknowledgments
This work was financially supported by the National Defense Basic Scientific Research Program (Grant Nos.
211-CXCY-N103-03-04-00 and 2022-JCKY-JJ-1086) and the National Natural Science Foundation of China
(Grant No. 52204343). First-principles calculations were performed on the clusters at Northwestern
Polytechnical University.
Authors’ contributions
Writing - original draft preparation, conceptualization, methodology, data curation, investigation, formal
analysis: Zhang, Y.
Writing - original draft preparation, supervision, methodology, editing, validation, project administration,
funding acquisition: Wang, W. Y.
Data curation, investigation, formal analysis, writing - original draft preparation: Wang, Y.; Ren, K.; Wang,
Z.
Conceptualization, methodology, editing, project administration: Zhang, K.
Supervision, conceptualization, methodology, editing, project administration: Gao, X.; Song, H.
Supervision, conceptualization, methodology, editing, project administration, funding acquisition: Liang, X.;
Li, J.